University of Nevada Reno Computational and Theoretical Modeling of Two Dimensional Infrared Spectra of Peptides and Proteins A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Chemical Physics by David. G Hogle Matthew J. Tucker/ Dissertation Advisior May 2019 i Abstract Two-dimensional infrared (2D-IR) spectroscopy evolved out of the theoretical underpinnings of nonlinear methods to provide a means of investigating detailed molecular structure on ultrafast timescales. This opens up new possibilities for the study of protein folding and molecule-solvent interactions through greater spatial and temporal resolution. To study biomolecules, functional groups sensitive to the local environment known as infrared reporters are used to investigate activity at a particular site or sites of interest. Through these probes the analysis of dynamic species and site-specific structural information, previously inaccessible to direct observation, can elucidate key details of conformational changes that exert major influences on the activities of complex molecular systems. The broad objective of the research of the Tucker group is to obtain a description of the dynamic processes that lead to conformational changes at a chemical bond scale. A major component of 2D IR methods is the choice of vibrational probes used, which impacts the structural information provided about the larger surrounding environment. The type and placement of infrared reporter is highly system-specific, and developments within this area continue to open up new areas of inquiry for 2D IR experiments. My work has been towards providing an understanding of how these probes interact with their surroundings for the purpose of rational infrared probe design and insertion. The use of non-natural amino acid side chain probes has shown promise for use in tracking the dynamics of the side chain region of proteins. Studies performed in this work have demonstrated the ability of local amino acid modes to capture changes in local electric fields and the degree of hydration at distinct locations in proteins. The ring mode of tyrosine has particular utility as a naturally occurring probe that shows a high degree of sensitivity to its environment through ii solvent broadening, giving rise to applications in studies of folded and unfolded peptides/proteins. This is a promising step towards expanding the tools available to observe solvation and van der Waals forces during enzymatic and membrane-binding processes, amongst others. We have investigated the interaction between two potentially useful reporters for use in in nucleotides and small peptides: the cyano- and the azido- moieties. Theoretical models developed using this data demonstrate opportunities for monitoring structural changes within oligonucleotides and peptides. The relations between the intensity of the coupling of these reporters with spatial orientation and distance allows mapping of groups on the sub-nanometer scale with a sub-picosecond time frame, taking advantage of the powerful time-resolution of infrared methods. The advance of two-dimensional infrared spectroscopy depends upon the development of new techniques that take full advantage of new technology and theoretical methods. My work with the Tucker groups has been towards the application of computational work towards understanding the relationship between the behavior of the molecular groups of interest and the data collected from the infrared beam. This will hopefully continue to open up new and exciting possibilities for the further expansion of infrared techniques, which are speculated on in the final section. These findings represent a step forward in the development of 2D IR probe groups for the investigation of sub-picosecond processes in biomolecules. iii Acknowledgements This journey has been an adventure, and like most actual adventures, I’m mainly thankful that it is almost over. I would like to affirm that graduate school is indeed rewarding, in its own way, although I believe the reward is mostly in moving on to other things. However, before I do, I would like to take the time to thank a few special people. Group members Amy Cunningham, Mat Roberson, Natalie Fetto, and Andrew Schimtz have been there with me and have been supportive over the years, and I doubt I would have achieved half as much without their assistance and support. While I took a year to make the decision to join the group, I was there near the start of the Tucker lab, so I had the opportunity to be there for much of the setup of the lab equipment. A major draw for this group was the chance to see the setup of a spectroscopy lab firsthand and in doing so learn about the techniques used in Two-dimensional infrared (2D-IR) spectroscopy, which I entered knowing next to nothing about except that infrared spectroscopy measures molecular vibrations. That seems so distant now; I have gained a broad knowledge base on the subject after working with it for almost five years, as well as the humbling realization of how much I still have yet so learn. One interesting thing about molecular movement is that all vibrational modes have a harmonic component, an idealized motion where the molecule moves in perfect periodicity. This is called a normal mode; and when undergoing periodic motion the molecule is said to move sinusoidally, which I thought sounded like something that’s gotten stuck up your nose. Interestingly, the etymological conflation here is due to a misunderstanding involving a Latin translation of a paper on trigonometry written in Arabic with Sanskrit words. Sinus in Latin means cavity (such as up iv your nose) and the common 'sinuses' are correctly referred to as the paranasal sinuses. So your nose has nothing to do with sine functions, which are sinusoidal, and hence nothing to sneeze at. A love of mathematics and a love of (allegedly terrible) puns have probably helped to me to persevere at my work when things didn’t seem to be terribly engaging. One of the truisms of science is that progress is often far more frustration and boredom than flashes of brilliant insight. The small victories in science, both personal and professional, are seldom celebrated or appreciated. Whether that is the modest success of me getting a particular code to run properly, or the slow, thankless progress of countless research groups developing the equipment and techniques over decades that I would base my work on, science is often a long, laborious process requiring countless setbacks and failed attempts before progress is made. Hopefully my own failed attempts and setbacks over the years have led to progress toward my own goals as well. I would be remiss if I did not thank my friends and family. During my years spent at UNR, several close associates offered words of wisdom, their friendship, and both academic and emotional support. Some of these people have since moved on to bigger and better things, while others are still waiting to finish their studies and their chance to move on. Jen Schimdt, Dylan Jones, and Keveen Flieth, thank you for your friendship and support. On perhaps a more personal level, I would like to thank Baron and Tyson, whose constant companionship has provided me the motivation to see this through. You guys mean more to me than most of those around me know, and I’ll always remember the time we spent together here in Nevada, and I look forward to doing more exciting science with both of you over the years v Abstract i Acknowledgements iii Table of Contents v List of Tables vii List of Figures viii Chapter 1: An Introduction to Infrared Spectroscopy 1 1.1 Basics of Infrared Spectroscopy 1.2 Emergence of Multidimensional Infrared Methods 1.3 2DIR Methods Allow for the Greater Exploration of Peptides Chapter 2: Models of Vibrational Interactions 17 2.1 Laser-Dipole interaction 2.2 Explanation of peak broadening and coupling 2.3 Computational Software Used 2.3.a Hessian and Gaussian Basis Sets 2.3.b Molecular Modeling Force Fields 2.4 Methods for measuring coupling 2.4.a Finite Difference Method 2.4.b Transition Dipole Coupling 2.4.c Transition Charge Model 2.4.d Transition Dipole Density Distribution 2.5 Solvent models 2.5.a Onsager model 2.5.b Conducting Polarizable Continuum Model Chapter 3: Azide and Nitrile Probes- The Best of Both Worlds 43 3.1 Theoretical Modeling of Novel Probe Behavior 3.2 Investigation of Conformational Preferences in 2’-azido-5-cyano-2’-deoxyuridine. 3.3 Modeling the Coupling Mechanism 3.4 Simulations of Azido and Nitrile Groups in a Model Peptide System 3.5 Conclusions and Future Directions Chapter 4: Molecular Dynamics Simulations with the Goal of Rational Probe Design 61 4.1 Development of Intrinsic Infrared Probes 4.2 Solvachromatic Effect of the Tyrosine Ring Mode 4.3 Theory and NAMD Simulations 4.4 Solvent Broadening Effects on the Tyrosine Ring Mode vi 4.5 Studies of Tyrosine as a Probe Involving the trp-Cage Peptide 4.6 Future Directions Chapter 5: Fermi Resonance in Para-azido-cyano Benzene 82 5.1 Introduction 5.2 Fermi resonance theory 5.3 Calculation of Mode Frequencies for Anharmonic Coupling. Chapter 6: Future Directions in 2D IR 96 6.1 Phenyalanine Derivatives 6.2 Future Probe Design 6.3 Transient 2D IR Methods 6.4 Conclusion Appendix A: Supplemental Information for the Theoretical Computation of Fermi Resonance 106 Appendix B: Matlab Code 108 Appendix C: Fortran Code 113 vii List of Tables Table 4.1 Solvatochromic effect on the tyrosine ring breathing vibrational transition Table 5.1 Results from simulated spectra to obtain cubic couplic terms viii List of Figures Figure 1.1 Typical transient 2D IR optical design with pulse shaping module Figure 1.2 Harmonic and anharmonic two-state excitation Figure 1.3 Typical 2D IR spectrum with coupled peaks Figure 2.1 Visual representation of Bloch dynamics Figure 2.2 A sample molecule of 2′-azido-5-cyano-2′-deoxyuridine molecule Figure 2.3 Two simple dipoles exerting forces on one another Figure 2.4 False color representation of two groups in a Transition Dipole Density Distribution Figure 2.5 Visualization of the Onsager field model Figure 3.1 Structure of the 2′-azido-2′-deoxyuridine molecule Figure 3.2 Comparison of Onsager and CPCM model.